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Strongly weak idempotent nil -clean rings | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 1، مهر 2025، صفحه 159-172 اصل مقاله (176.65 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.25294.1570 | ||
| نویسندگان | ||
| B. Asmare1؛ T. Abebaw1؛ K. Venkateswarlu* 2 | ||
| 1Department of Mathematics, College of Natural and Computational Science, Addis Ababa University, Addis Ababa, Ethiopia | ||
| 2Department of Computer Science and Systems Engineering, College of Engineering, Andhra University, Visakhapatnam, Andhra Pradesh, India | ||
| چکیده | ||
| We introduce the concept of strongly weak idempotent nil-clean rings which is a generalization of strongly weakly nil clean rings. We characterize strongly weak idempotent nil-clean rings in terms of the set of nilpotent elements, homomorphic images, and Jacobson radicals. We prove that a ring $R$ is strongly weak idempotent nil-clean if and only if for any $a\in R$, $a-a^3$ is nilpotent if and only if $Nil(R)$ forms an ideal and $R/{Nil(R)}$ is reduced weak idempotent nil-clean if and only if $R$ has no homomorphic image $\mathbb{Z}_3\oplus \mathbb{Z}_3$ and $a^2-a^4$ is nilpotent. Moreover, we prove that a strongly weak idempotent nil-clean ring $R$ with $2\in J(R)$ satisfies nil-involution property. | ||
| کلیدواژه‌ها | ||
| Strongly weakly nil clean rings؛ Strongly weak idempotent nil-clean rings؛ Strongly $\pi$-regular rings؛ Strongly clean rings؛ nil-involution | ||
| مراجع | ||
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[1] S. Breaz, P. Danchev and Y. Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, Journal of Algebra and its Applications, (8) 15 (2016), 1650148. [2] M. Chacron, On a theorem of Herstein, Canadian Journal of Mathematics, 21 (1969), 1348–1353. [3] H. Chen and M. Sheibani, Strongly weakly nil-clean rings, Journal of Algebra and Its Applications, (12) 16 (2017), 1750233. [4] J. Cui and P. Danchev, Some new characterizations of periodic rings, Journal of Algebra and Its Applications, (12) 19 (2020), 2050235. [5] A. J. Diesl, Nil clean rings, Journal of algebra, 383 (2013), 197–211. [6] A. J. Diesl, et al, A note on completeness and strongly clean rings, Journal of Pure and Applied Algebra, (4) 218 (2014), 661–665. [7] Y. Hirano, H. Tominaga and A. Yaqub, On rings in which every element is uniquely expressible as a sum of a nilpotent element and a certain potent element, Mathematical Journal of Okayama University, (1) 30 (1988), 33–40. [8] Z. Ying and J. Chen, On quasipolar rings, Algebra Colloquium, (4) 19 (2012), 683–692. | ||
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آمار تعداد مشاهده مقاله: 214 تعداد دریافت فایل اصل مقاله: 35 |
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